Problems for Practice

PROBLEMS FOR PRACTICE

For cantilever beams

1. A cantilever beam of length 1.5m carries a point load of 3 kN at its free end and another load of 2 kN at a distance of 1m from the fixed end. Draw the SF and BM diagrams for the cantilever.

2. A cantilever beam of length 5m carries point loads of 3 kN, 4 kN and 6 kN at 0, 2 and 3.5m from the free end. Draw the SFD and BMD for the cantilever.

3. A cantilever of length 4m carries a UDL of 3 kN/m over the whole length. Draw the SFD and BMD.

4. A cantilever of length 2m carries a uniformly distributed load of 3 kN/m over a length of 1m from the fixed end. Draw the SFD and BMD.

5. A cantilever of length 1.5m carries a UDL of 4 kN/m run over a length 1 m from the free end. Draw the SFD and BMD.

6. A cantilever of length 2.5m carries a UDL of 2 kN/m over the whole length and a point of 3 kN at the free end. Draw the SF and BM diagrams. If the point load of the same 3 kN acts at a distance of 1m from the fixed. Draw the SF and BM diagram for the cantilever with same UDL.

7. A cantilever of 3m long is loaded with a UDL of 3 kN/m run over a length of 1.5m from the free end. It also carries a point load of 3 kN at a distance of 1 m from the free end. Draw the SFD and BMD.

8. A cantilever of length 6m carries two point loads of 3 kN and 4 kN at a distance of 1m and 6m from the fixed end respectively. In addition to this, the beam also carries a UDL of 3 kN/m over a length of 2m at a distance of 3m from the fixed end. Draw the SFD and BMD.

9. A beam is loaded as shown in Fig. Draw the SFD and BMD.

10. A cantilever of length 6m carries a gradually varying load, zero at the free end to 3 kN/m at the fixed end. Draw the SF and BM diagrams,

For Simply supported beams:

11. Draw SF and BM diagrams for a cantilever beam 2m long carrying a gradually varying load from zero at the free end to 2000 N/m at the fixed end.

12. A SS beam of 5m long supported at the ends carries point loads of 140 kN, 60 KN and 80 kN at distances 0.5m, 2.5m and 3.5m respectively from the left support. Find the maximum, SF and BM diagrams and find maximum BM. 

13. A simply supported beam of 4m span carries a uniformly distributed load of 3 kN/m over the whole length of the beam. Draw SF and BM diagrams. 

14. A simply supported beam of 6m long is carrying a uniformly distributed load of 2 kN/m over a length of 3m from the right support. Draw the SF and BM diagrams for the beam and also calculate the maximum BM on the section. 

15. Draw the SF and BM diagrams for a SSB of 8m and carrying a uniformly distributed load of 10 kN/m for a distance of 5m from the left support. Also calculate the max. BM on the section.

16. Draw the SF and BM diagrams for the following SSB and also calculate maximum BM.

For overhanging beams:

17. A beam 10m long, supported over a span of 7m and having equal overhanging on both the sides, carries a concentrated load of 20 kN at one end and another concentrated load of 40 kN at the other end. Draw the SF and BM diagrams.

18. A beam ABCDE, 14m long, cantilevered over the portion AB 6m long, supported at points B and E, BE = 8m long, carries a concentrated load at end A, 3 tones at C, 3m from B and 5 tones at D, 2m from E. In addition it carries a UDL of 3 ton/m over the portion CD. Draw the SF and BM diagrams. Determine the position of point of contraflexure.

19. Draw the SF and BM diagrams of the beam shown in Fig. Show the location and magnitude of maximum bending moment.

20. Draw the SFD and BMD for the beam shown in the Figure and locate the point of contraflexure if any.

21. Draw the SF and BM diagram for the beam shown in Fig.

22. A horizontal beam AD, 8m long carries a UDL of 3 kN/m together with a concentrated load of 5 kN at the left end A. The beam is supported at a point B which is 2m from A and at C which is in the right hand half of the beam and 'x' m from D. Determine the value of x, if the midpoint of the beam is the point of contraflexure. Plot the SF and BM diagrams.

23. Draw to a convenient scale the diagrams of BM and SF for the beam supported and loaded as shown in sketch below. Show all principal values of BM and SF on the diagrams,

24. A horizontal beam simply supported by 5m length and overhang at the left end by 2.5m carries a UDL of 8 kN/m between the supports. Counter clockwise moment of 9 kN/m is applied at the left end. Draw the BMD and SFD and find 

(i) the reaction at the supports.

(ii) the position and magnitude of greatest bending moment.